# A Neural Symbolic Model for Space Physics

arXiv: https://arxiv.org/abs/2503.07994 · HTML: https://mlsanity.com/paper/2503.07994/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 73 references that are in the map.
- First posted on arXiv 11 Mar 2025.

## Builds on (most cited first, 26 of 26)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Deep Learning for Symbolic Mathematics](https://mlsanity.com/paper/1912.01412/) (2019)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [End-to-end symbolic regression with transformers](https://mlsanity.com/paper/2204.10532/) (2022)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity](https://mlsanity.com/paper/2006.10782/) (2020)
- [KAN 2.0: Kolmogorov-Arnold Networks Meet Science](https://mlsanity.com/paper/2408.10205/) (2024)
- [SymbolicGPT: A Generative Transformer Model for Symbolic Regression](https://mlsanity.com/paper/2106.14131/) (2021)
- [Symbolic Regression with a Learned Concept Library](https://mlsanity.com/paper/2409.09359/) (2024)
- [Transformer-based Planning for Symbolic Regression](https://mlsanity.com/paper/2303.06833/) (2023)
- [Bayesian Symbolic Regression](https://mlsanity.com/paper/1910.08892/) (2019)
- [Symbolic Physics Learner: Discovering governing equations via Monte Carlo tree search](https://mlsanity.com/paper/2205.13134/) (2022)
- [Linear algebra with transformers](https://mlsanity.com/paper/2112.01898/) (2021)
- [Deep symbolic regression for physics guided by units constraints: toward the automated discovery of physical laws](https://mlsanity.com/paper/2303.03192/) (2023)
- [Deep Generative Symbolic Regression with Monte-Carlo-Tree-Search](https://mlsanity.com/paper/2302.11223/) (2023)
- [Learning concise representations for regression by evolving networks of trees](https://mlsanity.com/paper/1807.00981/) (2018)
- [AI-Aristotle: A Physics-Informed framework for Systems Biology Gray-Box Identification](https://mlsanity.com/paper/2310.01433/) (2023)
- [Controllable Neural Symbolic Regression](https://mlsanity.com/paper/2304.10336/) (2023)
- [ParFam -- (Neural Guided) Symbolic Regression Based on Continuous Global Optimization](https://mlsanity.com/paper/2310.05537/) (2023)
- [AI-Lorenz: A physics-data-driven framework for black-box and gray-box identification of chaotic systems with symbolic regression](https://mlsanity.com/paper/2312.14237/) (2023)
- [RSRM: Reinforcement Symbolic Regression Machine](https://mlsanity.com/paper/2305.14656/) (2023)
- [Deep Optimizer States: Towards Scalable Training of Transformer Models Using Interleaved Offloading](https://mlsanity.com/paper/2410.21316/) (2024)
- [Bootstrapping OTS-Funcimg Pre-training Model (Botfip) -- A Comprehensive Symbolic Regression Framework](https://mlsanity.com/paper/2401.09748/) (2024)
- [An Efficient and Generalizable Symbolic Regression Method for Time Series Analysis](https://mlsanity.com/paper/2409.03986/) (2024)

## Built on by (most cited first, 11 of 11)

- [A Survey of Scientific Large Language Models: From Data Foundations to Agent Frontiers](https://mlsanity.com/paper/2508.21148/) (2025)
- [The Need for Verification in AI-Driven Scientific Discovery](https://mlsanity.com/paper/2509.01398/) (2025)
- [Data-driven discovery of governing differential equations across physical systems](https://mlsanity.com/paper/2606.09638/) (2026)
- [Beyond Accuracy and Complexity: The Effective Information Criterion for Structurally Stable Symbolic Regression](https://mlsanity.com/paper/2509.21780/) (2025)
- [The Machine Learning Approach to Moment Closure Relations for Plasma: A Review](https://mlsanity.com/paper/2511.22486/) (2025)
- [Prior-Guided Symbolic Regression: Towards Scientific Consistency in Equation Discovery](https://mlsanity.com/paper/2602.13021/) (2026)
- [Discover Fast Power Allocation Solution for Multi-Target Tracking via AlphaEvolve Evolution](https://mlsanity.com/paper/2605.01794/) (2026)
- [Evidence-Grounded Frontier Mapping and Agentic Hypothesis Generation in Nanomedicine](https://mlsanity.com/paper/2605.18144/) (2026)
- [Decision-Making under Combinatorial Risk](https://mlsanity.com/paper/2606.10092/) (2026)
- [Not Every Term Adds New Structure: Sobolev Novelty for Symbolic Regression](https://mlsanity.com/paper/2609.32597/) (2026)
- [Synthesizing Physics Formulae with Transformers](https://mlsanity.com/paper/2610.03947/) (2026)

## Abstract (arXiv)

In this study, we unveil a new AI model, termed PhyE2E, to discover physical formulas through symbolic regression. PhyE2E simplifies symbolic regression by decomposing it into sub-problems using the second-order derivatives of an oracle neural network, and employs a transformer model to translate data into symbolic formulas in an end-to-end manner. The resulting formulas are refined through Monte-Carlo Tree Search and Genetic Programming. We leverage a large language model to synthesize extensive symbolic expressions resembling real physics, and train the model to recover these formulas directly from data. A comprehensive evaluation reveals that PhyE2E outperforms existing state-of-the-art approaches, delivering superior symbolic accuracy, precision in data fitting, and consistency in physical units. We deployed PhyE2E to five applications in space physics, including the prediction of sunspot numbers, solar rotational angular velocity, emission line contribution functions, near-Earth plasma pressure, and lunar-tide plasma signals. The physical formulas generated by AI demonstrate a high degree of accuracy in fitting the experimental data from satellites and astronomical telescopes. We have successfully upgraded the formula proposed by NASA in 1993 regarding solar activity, and for the first time, provided the explanations for the long cycle of solar activity in an explicit form. We also found that the decay of near-Earth plasma pressure is proportional to r^2 to Earth, where subsequent mathematical derivations are consistent with satellite data from another independent study. Moreover, we found physical formulas that can describe the relationships between emission lines in the extreme ultraviolet spectrum of the Sun, temperatures, electron densities, and magnetic fields. The formula obtained is consistent with the properties that physicists had previously hypothesized it should possess.